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ahrayia [7]
3 years ago
15

Based on the type of equations in the system, what is the greatest possible number of solutions (x2+y2=9/9x+2y=16?

Mathematics
2 answers:
ozzi3 years ago
8 0

Answer:

`Option B.

Step-by-step explanation:

The given system of equations is

x^2+y^2=9

9x+2y=16

The graph of first equation is circle and the graph of second equation is a line.

We know that a line can intersect a circle at most 2 times. So, the greatest possible number of solutions is 2.

First equation can be rewritten as

x^2+y^2=3^2

It is the standard form of a circle (x-h)^2+(y-k)^2=r^2, where (h,k) is center and r is radius.

In the above equation h=0,k=0 and r=3. It is a circle with radius 3 and centered at origin.

The second equation is

9x+2y=16

It is a linear equation.

Table of values.

x    y

0    8

1     3.5

2    -1

Plot these points on a coordinate plane and connect them by a straight line.

From the below graph it is clear that the line and circle intersect each other at two points. So, the given system of equation have two solutions.

Therefore, the correct option is B.

Rama09 [41]3 years ago
5 0

Answer:

c the waydeez

Step-by-step explanation:

explanations n more to coke

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I don't know what c you are talking about because there is no picture
4 0
3 years ago
Question 2 of 10
AnnyKZ [126]

The length of AB will be 10 units. Option B is corect. The formula for the distance between the two points is applied in a given problem.

<h3>What is the distance between the two points?</h3>

The length of the line segment connecting two places is the distance between them.

The distance between two places is always positive, and equal-length segments are referred to as congruent segments.

The given coordinate in the problem is;

(x₁,y₁)=(-2,-4)

(x₂, y₂)= (-8, 4)

The distance between the two points is found as;

\rm d= \sqrt{(-8-(-2))^2+(4-(-4))^2}\\\\ d=10 \ units

Hence, option B is corect.

To learn more about the distance between the two points, refer to;

brainly.com/question/16410393

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4 0
2 years ago
The cost for an order of 100 kilograms of steel bars is $230. The cost for an order of 150 kilograms of steel bars is $320. Writ
luda_lava [24]

Answer:

y = 9x/5 + 50

Step-by-step explanation:

We are represent the information as coordinate (x,y)

If the cost for an order of 100 kilograms of steel bars is $230, this is expressed as (100, 230)

Also if the cost for an order of 150 kilograms of steel bars is $320, this is expressed as;

(150, 320)

Find the equation of a line passing through the points. The standard form of the equation is expressed as y = mx+c

m is the slope

c is the intercept

Get the slope;

m = y2-y1/x2-x1

m = 320-230/150-100

m = 90/50

m = 9/5

Get the y-intercept by substituting m = 9/5 and any point say (100, 230) into the expression y = mx+c

230 = 9/5(100)+c

230 = 9(20)+c

230 = 180 + c

c = 230-180

c = 50

Get the required equation

y = mx+c

y = 9/5 x + 50

Hence an equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x) is y = 9x/5 + 50

4 0
3 years ago
Write the equation of the line that passes through (−1, 5) and has a slope of 3 in point-slope form. (2 points)
aleksandr82 [10.1K]
The point-slope form: y-y_0=m(x-x_0)

m = 3; (-1; 5) \to x_0=-1;\ y_0=5

subtitute

y - 5 = 3(x - (-1))

y - 5 = 3(x + 1)
4 0
3 years ago
Read 2 more answers
Elevii clasei a IV-a au fost la patinoar. Stiind ca numarul baietilor reprezinta jumatate plus 3 din numarul copiilor si ca numa
Shalnov [3]

Step-by-step explanation:

Fie x numărul de copii

f = 10 =\:fete

b\:=\:\frac{x}{2}\:+\:3

f\:+\:b\:=\:x

10\:+\:\frac{x}{2}\:+\:3\:=\:x

20\:+\:x\:+\:6\:=\:2x

x\:=\:26\:copii\:au\:fost\:la\:patinoar

b=\frac{26}{2}+\:3

b\:=\:16\:baieti

7 0
3 years ago
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